// Copyright (C) 2012  Davis E. King (davis@dlib.net)
// License: Boost Software License   See LICENSE.txt for the full license.
#ifndef DLIB_RANDOM_HAsHING_Hh_ 
#define DLIB_RANDOM_HAsHING_Hh_ 

#include "random_hashing_abstract.h"
#include "murmur_hash3.h"

namespace dlib
{

// ----------------------------------------------------------------------------------------

    inline double uniform_random_hash (
        const uint64& k1,
        const uint64& k2,
        const uint64& k3
    )
    {
        const std::pair<uint64,uint64> h = murmur_hash3_128bit_3(k1,k2,k3);
        const uint64 mask = DLIB_BIG_CONSTANT(0xFFFFFFFFFF); 
        const double max = mask+1;
        return static_cast<double>(h.first&mask)/max;
    }

// ----------------------------------------------------------------------------------------

    inline double gaussian_random_hash (
        const uint64& k1,
        const uint64& k2,
        const uint64& k3
    )
    {
        const std::pair<uint64,uint64> h = murmur_hash3_128bit_3(k1,k2,k3);

        const static unsigned int max = 4096;

        const static double logvals[max] = { 
        4.079, 3.905, 3.8, 3.723, 3.663, 3.613, 3.57, 3.532, 3.499, 3.468, 
        3.441, 3.416, 3.392, 3.37, 3.35, 3.33, 3.312, 3.295, 3.278, 3.263, 
        3.248, 3.233, 3.219, 3.206, 3.193, 3.181, 3.169, 3.158, 3.147, 3.136, 
        3.125, 3.115, 3.105, 3.096, 3.086, 3.077, 3.068, 3.059, 3.051, 3.043, 
        3.035, 3.027, 3.019, 3.011, 3.004, 2.996, 2.989, 2.982, 2.975, 2.968, 
        2.962, 2.955, 2.949, 2.942, 2.936, 2.93, 2.924, 2.918, 2.912, 2.906, 
        2.901, 2.895, 2.89, 2.884, 2.879, 2.873, 2.868, 2.863, 2.858, 2.853, 
        2.848, 2.843, 2.838, 2.833, 2.829, 2.824, 2.819, 2.815, 2.81, 2.806, 
        2.801, 2.797, 2.792, 2.788, 2.784, 2.78, 2.776, 2.771, 2.767, 2.763, 
        2.759, 2.755, 2.751, 2.748, 2.744, 2.74, 2.736, 2.732, 2.729, 2.725, 
        2.721, 2.718, 2.714, 2.71, 2.707, 2.703, 2.7, 2.697, 2.693, 2.69, 
        2.686, 2.683, 2.68, 2.676, 2.673, 2.67, 2.667, 2.663, 2.66, 2.657, 
        2.654, 2.651, 2.648, 2.645, 2.642, 2.639, 2.636, 2.633, 2.63, 2.627, 
        2.624, 2.621, 2.618, 2.615, 2.612, 2.61, 2.607, 2.604, 2.601, 2.599, 
        2.596, 2.593, 2.59, 2.588, 2.585, 2.582, 2.58, 2.577, 2.574, 2.572, 
        2.569, 2.567, 2.564, 2.562, 2.559, 2.557, 2.554, 2.552, 2.549, 2.547, 
        2.544, 2.542, 2.539, 2.537, 2.534, 2.532, 2.53, 2.527, 2.525, 2.523, 
        2.52, 2.518, 2.516, 2.513, 2.511, 2.509, 2.507, 2.504, 2.502, 2.5, 
        2.498, 2.495, 2.493, 2.491, 2.489, 2.487, 2.485, 2.482, 2.48, 2.478, 
        2.476, 2.474, 2.472, 2.47, 2.468, 2.466, 2.464, 2.462, 2.459, 2.457, 
        2.455, 2.453, 2.451, 2.449, 2.447, 2.445, 2.443, 2.441, 2.439, 2.437, 
        2.436, 2.434, 2.432, 2.43, 2.428, 2.426, 2.424, 2.422, 2.42, 2.418, 
        2.416, 2.415, 2.413, 2.411, 2.409, 2.407, 2.405, 2.404, 2.402, 2.4, 
        2.398, 2.396, 2.394, 2.393, 2.391, 2.389, 2.387, 2.386, 2.384, 2.382, 
        2.38, 2.379, 2.377, 2.375, 2.373, 2.372, 2.37, 2.368, 2.367, 2.365, 
        2.363, 2.361, 2.36, 2.358, 2.356, 2.355, 2.353, 2.352, 2.35, 2.348, 
        2.347, 2.345, 2.343, 2.342, 2.34, 2.338, 2.337, 2.335, 2.334, 2.332, 
        2.331, 2.329, 2.327, 2.326, 2.324, 2.323, 2.321, 2.32, 2.318, 2.316, 
        2.315, 2.313, 2.312, 2.31, 2.309, 2.307, 2.306, 2.304, 2.303, 2.301, 
        2.3, 2.298, 2.297, 2.295, 2.294, 2.292, 2.291, 2.289, 2.288, 2.286, 
        2.285, 2.284, 2.282, 2.281, 2.279, 2.278, 2.276, 2.275, 2.274, 2.272, 
        2.271, 2.269, 2.268, 2.266, 2.265, 2.264, 2.262, 2.261, 2.259, 2.258, 
        2.257, 2.255, 2.254, 2.253, 2.251, 2.25, 2.248, 2.247, 2.246, 2.244, 
        2.243, 2.242, 2.24, 2.239, 2.238, 2.236, 2.235, 2.234, 2.232, 2.231, 
        2.23, 2.228, 2.227, 2.226, 2.225, 2.223, 2.222, 2.221, 2.219, 2.218, 
        2.217, 2.215, 2.214, 2.213, 2.212, 2.21, 2.209, 2.208, 2.207, 2.205, 
        2.204, 2.203, 2.202, 2.2, 2.199, 2.198, 2.197, 2.195, 2.194, 2.193, 
        2.192, 2.19, 2.189, 2.188, 2.187, 2.185, 2.184, 2.183, 2.182, 2.181, 
        2.179, 2.178, 2.177, 2.176, 2.175, 2.173, 2.172, 2.171, 2.17, 2.169, 
        2.168, 2.166, 2.165, 2.164, 2.163, 2.162, 2.16, 2.159, 2.158, 2.157, 
        2.156, 2.155, 2.154, 2.152, 2.151, 2.15, 2.149, 2.148, 2.147, 2.146, 
        2.144, 2.143, 2.142, 2.141, 2.14, 2.139, 2.138, 2.136, 2.135, 2.134, 
        2.133, 2.132, 2.131, 2.13, 2.129, 2.128, 2.126, 2.125, 2.124, 2.123, 
        2.122, 2.121, 2.12, 2.119, 2.118, 2.117, 2.116, 2.114, 2.113, 2.112, 
        2.111, 2.11, 2.109, 2.108, 2.107, 2.106, 2.105, 2.104, 2.103, 2.102, 
        2.101, 2.1, 2.099, 2.097, 2.096, 2.095, 2.094, 2.093, 2.092, 2.091, 
        2.09, 2.089, 2.088, 2.087, 2.086, 2.085, 2.084, 2.083, 2.082, 2.081, 
        2.08, 2.079, 2.078, 2.077, 2.076, 2.075, 2.074, 2.073, 2.072, 2.071, 
        2.07, 2.069, 2.068, 2.067, 2.066, 2.065, 2.064, 2.063, 2.062, 2.061, 
        2.06, 2.059, 2.058, 2.057, 2.056, 2.055, 2.054, 2.053, 2.052, 2.051, 
        2.05, 2.049, 2.048, 2.047, 2.046, 2.045, 2.044, 2.043, 2.042, 2.041, 
        2.04, 2.039, 2.038, 2.037, 2.036, 2.036, 2.035, 2.034, 2.033, 2.032, 
        2.031, 2.03, 2.029, 2.028, 2.027, 2.026, 2.025, 2.024, 2.023, 2.022, 
        2.021, 2.02, 2.02, 2.019, 2.018, 2.017, 2.016, 2.015, 2.014, 2.013, 
        2.012, 2.011, 2.01, 2.009, 2.008, 2.008, 2.007, 2.006, 2.005, 2.004, 
        2.003, 2.002, 2.001, 2, 1.999, 1.998, 1.998, 1.997, 1.996, 1.995, 
        1.994, 1.993, 1.992, 1.991, 1.99, 1.99, 1.989, 1.988, 1.987, 1.986, 
        1.985, 1.984, 1.983, 1.982, 1.982, 1.981, 1.98, 1.979, 1.978, 1.977, 
        1.976, 1.975, 1.975, 1.974, 1.973, 1.972, 1.971, 1.97, 1.969, 1.969, 
        1.968, 1.967, 1.966, 1.965, 1.964, 1.963, 1.963, 1.962, 1.961, 1.96, 
        1.959, 1.958, 1.957, 1.957, 1.956, 1.955, 1.954, 1.953, 1.952, 1.952, 
        1.951, 1.95, 1.949, 1.948, 1.947, 1.947, 1.946, 1.945, 1.944, 1.943, 
        1.942, 1.942, 1.941, 1.94, 1.939, 1.938, 1.937, 1.937, 1.936, 1.935, 
        1.934, 1.933, 1.933, 1.932, 1.931, 1.93, 1.929, 1.928, 1.928, 1.927, 
        1.926, 1.925, 1.924, 1.924, 1.923, 1.922, 1.921, 1.92, 1.92, 1.919, 
        1.918, 1.917, 1.916, 1.916, 1.915, 1.914, 1.913, 1.912, 1.912, 1.911, 
        1.91, 1.909, 1.908, 1.908, 1.907, 1.906, 1.905, 1.904, 1.904, 1.903, 
        1.902, 1.901, 1.901, 1.9, 1.899, 1.898, 1.897, 1.897, 1.896, 1.895, 
        1.894, 1.894, 1.893, 1.892, 1.891, 1.89, 1.89, 1.889, 1.888, 1.887, 
        1.887, 1.886, 1.885, 1.884, 1.884, 1.883, 1.882, 1.881, 1.88, 1.88, 
        1.879, 1.878, 1.877, 1.877, 1.876, 1.875, 1.874, 1.874, 1.873, 1.872, 
        1.871, 1.871, 1.87, 1.869, 1.868, 1.868, 1.867, 1.866, 1.865, 1.865, 
        1.864, 1.863, 1.862, 1.862, 1.861, 1.86, 1.859, 1.859, 1.858, 1.857, 
        1.857, 1.856, 1.855, 1.854, 1.854, 1.853, 1.852, 1.851, 1.851, 1.85, 
        1.849, 1.848, 1.848, 1.847, 1.846, 1.846, 1.845, 1.844, 1.843, 1.843, 
        1.842, 1.841, 1.84, 1.84, 1.839, 1.838, 1.838, 1.837, 1.836, 1.835, 
        1.835, 1.834, 1.833, 1.833, 1.832, 1.831, 1.83, 1.83, 1.829, 1.828, 
        1.828, 1.827, 1.826, 1.825, 1.825, 1.824, 1.823, 1.823, 1.822, 1.821, 
        1.821, 1.82, 1.819, 1.818, 1.818, 1.817, 1.816, 1.816, 1.815, 1.814, 
        1.814, 1.813, 1.812, 1.811, 1.811, 1.81, 1.809, 1.809, 1.808, 1.807, 
        1.807, 1.806, 1.805, 1.805, 1.804, 1.803, 1.802, 1.802, 1.801, 1.8, 
        1.8, 1.799, 1.798, 1.798, 1.797, 1.796, 1.796, 1.795, 1.794, 1.794, 
        1.793, 1.792, 1.792, 1.791, 1.79, 1.79, 1.789, 1.788, 1.787, 1.787, 
        1.786, 1.785, 1.785, 1.784, 1.783, 1.783, 1.782, 1.781, 1.781, 1.78, 
        1.779, 1.779, 1.778, 1.777, 1.777, 1.776, 1.775, 1.775, 1.774, 1.773, 
        1.773, 1.772, 1.771, 1.771, 1.77, 1.769, 1.769, 1.768, 1.767, 1.767, 
        1.766, 1.766, 1.765, 1.764, 1.764, 1.763, 1.762, 1.762, 1.761, 1.76, 
        1.76, 1.759, 1.758, 1.758, 1.757, 1.756, 1.756, 1.755, 1.754, 1.754, 
        1.753, 1.752, 1.752, 1.751, 1.751, 1.75, 1.749, 1.749, 1.748, 1.747, 
        1.747, 1.746, 1.745, 1.745, 1.744, 1.743, 1.743, 1.742, 1.742, 1.741, 
        1.74, 1.74, 1.739, 1.738, 1.738, 1.737, 1.736, 1.736, 1.735, 1.735, 
        1.734, 1.733, 1.733, 1.732, 1.731, 1.731, 1.73, 1.729, 1.729, 1.728, 
        1.728, 1.727, 1.726, 1.726, 1.725, 1.724, 1.724, 1.723, 1.723, 1.722, 
        1.721, 1.721, 1.72, 1.719, 1.719, 1.718, 1.718, 1.717, 1.716, 1.716, 
        1.715, 1.715, 1.714, 1.713, 1.713, 1.712, 1.711, 1.711, 1.71, 1.71, 
        1.709, 1.708, 1.708, 1.707, 1.706, 1.706, 1.705, 1.705, 1.704, 1.703, 
        1.703, 1.702, 1.702, 1.701, 1.7, 1.7, 1.699, 1.699, 1.698, 1.697, 
        1.697, 1.696, 1.696, 1.695, 1.694, 1.694, 1.693, 1.692, 1.692, 1.691, 
        1.691, 1.69, 1.689, 1.689, 1.688, 1.688, 1.687, 1.686, 1.686, 1.685, 
        1.685, 1.684, 1.683, 1.683, 1.682, 1.682, 1.681, 1.68, 1.68, 1.679, 
        1.679, 1.678, 1.678, 1.677, 1.676, 1.676, 1.675, 1.675, 1.674, 1.673, 
        1.673, 1.672, 1.672, 1.671, 1.67, 1.67, 1.669, 1.669, 1.668, 1.667, 
        1.667, 1.666, 1.666, 1.665, 1.665, 1.664, 1.663, 1.663, 1.662, 1.662, 
        1.661, 1.66, 1.66, 1.659, 1.659, 1.658, 1.658, 1.657, 1.656, 1.656, 
        1.655, 1.655, 1.654, 1.653, 1.653, 1.652, 1.652, 1.651, 1.651, 1.65, 
        1.649, 1.649, 1.648, 1.648, 1.647, 1.647, 1.646, 1.645, 1.645, 1.644, 
        1.644, 1.643, 1.643, 1.642, 1.641, 1.641, 1.64, 1.64, 1.639, 1.639, 
        1.638, 1.637, 1.637, 1.636, 1.636, 1.635, 1.635, 1.634, 1.633, 1.633, 
        1.632, 1.632, 1.631, 1.631, 1.63, 1.629, 1.629, 1.628, 1.628, 1.627, 
        1.627, 1.626, 1.625, 1.625, 1.624, 1.624, 1.623, 1.623, 1.622, 1.622, 
        1.621, 1.62, 1.62, 1.619, 1.619, 1.618, 1.618, 1.617, 1.617, 1.616, 
        1.615, 1.615, 1.614, 1.614, 1.613, 1.613, 1.612, 1.612, 1.611, 1.61, 
        1.61, 1.609, 1.609, 1.608, 1.608, 1.607, 1.607, 1.606, 1.605, 1.605, 
        1.604, 1.604, 1.603, 1.603, 1.602, 1.602, 1.601, 1.6, 1.6, 1.599, 
        1.599, 1.598, 1.598, 1.597, 1.597, 1.596, 1.596, 1.595, 1.594, 1.594, 
        1.593, 1.593, 1.592, 1.592, 1.591, 1.591, 1.59, 1.59, 1.589, 1.588, 
        1.588, 1.587, 1.587, 1.586, 1.586, 1.585, 1.585, 1.584, 1.584, 1.583, 
        1.582, 1.582, 1.581, 1.581, 1.58, 1.58, 1.579, 1.579, 1.578, 1.578, 
        1.577, 1.577, 1.576, 1.576, 1.575, 1.574, 1.574, 1.573, 1.573, 1.572, 
        1.572, 1.571, 1.571, 1.57, 1.57, 1.569, 1.569, 1.568, 1.567, 1.567, 
        1.566, 1.566, 1.565, 1.565, 1.564, 1.564, 1.563, 1.563, 1.562, 1.562, 
        1.561, 1.561, 1.56, 1.56, 1.559, 1.558, 1.558, 1.557, 1.557, 1.556, 
        1.556, 1.555, 1.555, 1.554, 1.554, 1.553, 1.553, 1.552, 1.552, 1.551, 
        1.551, 1.55, 1.55, 1.549, 1.549, 1.548, 1.547, 1.547, 1.546, 1.546, 
        1.545, 1.545, 1.544, 1.544, 1.543, 1.543, 1.542, 1.542, 1.541, 1.541, 
        1.54, 1.54, 1.539, 1.539, 1.538, 1.538, 1.537, 1.537, 1.536, 1.536, 
        1.535, 1.534, 1.534, 1.533, 1.533, 1.532, 1.532, 1.531, 1.531, 1.53, 
        1.53, 1.529, 1.529, 1.528, 1.528, 1.527, 1.527, 1.526, 1.526, 1.525, 
        1.525, 1.524, 1.524, 1.523, 1.523, 1.522, 1.522, 1.521, 1.521, 1.52, 
        1.52, 1.519, 1.519, 1.518, 1.518, 1.517, 1.517, 1.516, 1.516, 1.515, 
        1.515, 1.514, 1.514, 1.513, 1.512, 1.512, 1.511, 1.511, 1.51, 1.51, 
        1.509, 1.509, 1.508, 1.508, 1.507, 1.507, 1.506, 1.506, 1.505, 1.505, 
        1.504, 1.504, 1.503, 1.503, 1.502, 1.502, 1.501, 1.501, 1.5, 1.5, 
        1.499, 1.499, 1.498, 1.498, 1.497, 1.497, 1.496, 1.496, 1.495, 1.495, 
        1.494, 1.494, 1.493, 1.493, 1.492, 1.492, 1.491, 1.491, 1.49, 1.49, 
        1.489, 1.489, 1.488, 1.488, 1.487, 1.487, 1.486, 1.486, 1.485, 1.485, 
        1.484, 1.484, 1.483, 1.483, 1.482, 1.482, 1.481, 1.481, 1.48, 1.48, 
        1.48, 1.479, 1.479, 1.478, 1.478, 1.477, 1.477, 1.476, 1.476, 1.475, 
        1.475, 1.474, 1.474, 1.473, 1.473, 1.472, 1.472, 1.471, 1.471, 1.47, 
        1.47, 1.469, 1.469, 1.468, 1.468, 1.467, 1.467, 1.466, 1.466, 1.465, 
        1.465, 1.464, 1.464, 1.463, 1.463, 1.462, 1.462, 1.461, 1.461, 1.46, 
        1.46, 1.459, 1.459, 1.458, 1.458, 1.458, 1.457, 1.457, 1.456, 1.456, 
        1.455, 1.455, 1.454, 1.454, 1.453, 1.453, 1.452, 1.452, 1.451, 1.451, 
        1.45, 1.45, 1.449, 1.449, 1.448, 1.448, 1.447, 1.447, 1.446, 1.446, 
        1.445, 1.445, 1.444, 1.444, 1.444, 1.443, 1.443, 1.442, 1.442, 1.441, 
        1.441, 1.44, 1.44, 1.439, 1.439, 1.438, 1.438, 1.437, 1.437, 1.436, 
        1.436, 1.435, 1.435, 1.434, 1.434, 1.434, 1.433, 1.433, 1.432, 1.432, 
        1.431, 1.431, 1.43, 1.43, 1.429, 1.429, 1.428, 1.428, 1.427, 1.427, 
        1.426, 1.426, 1.425, 1.425, 1.424, 1.424, 1.424, 1.423, 1.423, 1.422, 
        1.422, 1.421, 1.421, 1.42, 1.42, 1.419, 1.419, 1.418, 1.418, 1.417, 
        1.417, 1.416, 1.416, 1.416, 1.415, 1.415, 1.414, 1.414, 1.413, 1.413, 
        1.412, 1.412, 1.411, 1.411, 1.41, 1.41, 1.409, 1.409, 1.409, 1.408, 
        1.408, 1.407, 1.407, 1.406, 1.406, 1.405, 1.405, 1.404, 1.404, 1.403, 
        1.403, 1.402, 1.402, 1.402, 1.401, 1.401, 1.4, 1.4, 1.399, 1.399, 
        1.398, 1.398, 1.397, 1.397, 1.396, 1.396, 1.395, 1.395, 1.395, 1.394, 
        1.394, 1.393, 1.393, 1.392, 1.392, 1.391, 1.391, 1.39, 1.39, 1.389, 
        1.389, 1.389, 1.388, 1.388, 1.387, 1.387, 1.386, 1.386, 1.385, 1.385, 
        1.384, 1.384, 1.383, 1.383, 1.383, 1.382, 1.382, 1.381, 1.381, 1.38, 
        1.38, 1.379, 1.379, 1.378, 1.378, 1.378, 1.377, 1.377, 1.376, 1.376, 
        1.375, 1.375, 1.374, 1.374, 1.373, 1.373, 1.373, 1.372, 1.372, 1.371, 
        1.371, 1.37, 1.37, 1.369, 1.369, 1.368, 1.368, 1.367, 1.367, 1.367, 
        1.366, 1.366, 1.365, 1.365, 1.364, 1.364, 1.363, 1.363, 1.362, 1.362, 
        1.362, 1.361, 1.361, 1.36, 1.36, 1.359, 1.359, 1.358, 1.358, 1.358, 
        1.357, 1.357, 1.356, 1.356, 1.355, 1.355, 1.354, 1.354, 1.353, 1.353, 
        1.353, 1.352, 1.352, 1.351, 1.351, 1.35, 1.35, 1.349, 1.349, 1.349, 
        1.348, 1.348, 1.347, 1.347, 1.346, 1.346, 1.345, 1.345, 1.344, 1.344, 
        1.344, 1.343, 1.343, 1.342, 1.342, 1.341, 1.341, 1.34, 1.34, 1.34, 
        1.339, 1.339, 1.338, 1.338, 1.337, 1.337, 1.336, 1.336, 1.336, 1.335, 
        1.335, 1.334, 1.334, 1.333, 1.333, 1.332, 1.332, 1.332, 1.331, 1.331, 
        1.33, 1.33, 1.329, 1.329, 1.328, 1.328, 1.328, 1.327, 1.327, 1.326, 
        1.326, 1.325, 1.325, 1.324, 1.324, 1.324, 1.323, 1.323, 1.322, 1.322, 
        1.321, 1.321, 1.32, 1.32, 1.32, 1.319, 1.319, 1.318, 1.318, 1.317, 
        1.317, 1.316, 1.316, 1.316, 1.315, 1.315, 1.314, 1.314, 1.313, 1.313, 
        1.312, 1.312, 1.312, 1.311, 1.311, 1.31, 1.31, 1.309, 1.309, 1.309, 
        1.308, 1.308, 1.307, 1.307, 1.306, 1.306, 1.305, 1.305, 1.305, 1.304, 
        1.304, 1.303, 1.303, 1.302, 1.302, 1.302, 1.301, 1.301, 1.3, 1.3, 
        1.299, 1.299, 1.298, 1.298, 1.298, 1.297, 1.297, 1.296, 1.296, 1.295, 
        1.295, 1.295, 1.294, 1.294, 1.293, 1.293, 1.292, 1.292, 1.291, 1.291, 
        1.291, 1.29, 1.29, 1.289, 1.289, 1.288, 1.288, 1.288, 1.287, 1.287, 
        1.286, 1.286, 1.285, 1.285, 1.285, 1.284, 1.284, 1.283, 1.283, 1.282, 
        1.282, 1.281, 1.281, 1.281, 1.28, 1.28, 1.279, 1.279, 1.278, 1.278, 
        1.278, 1.277, 1.277, 1.276, 1.276, 1.275, 1.275, 1.275, 1.274, 1.274, 
        1.273, 1.273, 1.272, 1.272, 1.272, 1.271, 1.271, 1.27, 1.27, 1.269, 
        1.269, 1.269, 1.268, 1.268, 1.267, 1.267, 1.266, 1.266, 1.266, 1.265, 
        1.265, 1.264, 1.264, 1.263, 1.263, 1.263, 1.262, 1.262, 1.261, 1.261, 
        1.26, 1.26, 1.26, 1.259, 1.259, 1.258, 1.258, 1.257, 1.257, 1.257, 
        1.256, 1.256, 1.255, 1.255, 1.254, 1.254, 1.254, 1.253, 1.253, 1.252, 
        1.252, 1.251, 1.251, 1.251, 1.25, 1.25, 1.249, 1.249, 1.248, 1.248, 
        1.248, 1.247, 1.247, 1.246, 1.246, 1.245, 1.245, 1.245, 1.244, 1.244, 
        1.243, 1.243, 1.242, 1.242, 1.242, 1.241, 1.241, 1.24, 1.24, 1.239, 
        1.239, 1.239, 1.238, 1.238, 1.237, 1.237, 1.237, 1.236, 1.236, 1.235, 
        1.235, 1.234, 1.234, 1.234, 1.233, 1.233, 1.232, 1.232, 1.231, 1.231, 
        1.231, 1.23, 1.23, 1.229, 1.229, 1.228, 1.228, 1.228, 1.227, 1.227, 
        1.226, 1.226, 1.226, 1.225, 1.225, 1.224, 1.224, 1.223, 1.223, 1.223, 
        1.222, 1.222, 1.221, 1.221, 1.22, 1.22, 1.22, 1.219, 1.219, 1.218, 
        1.218, 1.218, 1.217, 1.217, 1.216, 1.216, 1.215, 1.215, 1.215, 1.214, 
        1.214, 1.213, 1.213, 1.212, 1.212, 1.212, 1.211, 1.211, 1.21, 1.21, 
        1.21, 1.209, 1.209, 1.208, 1.208, 1.207, 1.207, 1.207, 1.206, 1.206, 
        1.205, 1.205, 1.204, 1.204, 1.204, 1.203, 1.203, 1.202, 1.202, 1.202, 
        1.201, 1.201, 1.2, 1.2, 1.199, 1.199, 1.199, 1.198, 1.198, 1.197, 
        1.197, 1.197, 1.196, 1.196, 1.195, 1.195, 1.194, 1.194, 1.194, 1.193, 
        1.193, 1.192, 1.192, 1.192, 1.191, 1.191, 1.19, 1.19, 1.189, 1.189, 
        1.189, 1.188, 1.188, 1.187, 1.187, 1.187, 1.186, 1.186, 1.185, 1.185, 
        1.184, 1.184, 1.184, 1.183, 1.183, 1.182, 1.182, 1.182, 1.181, 1.181, 
        1.18, 1.18, 1.179, 1.179, 1.179, 1.178, 1.178, 1.177, 1.177, 1.177, 
        1.176, 1.176, 1.175, 1.175, 1.175, 1.174, 1.174, 1.173, 1.173, 1.172, 
        1.172, 1.172, 1.171, 1.171, 1.17, 1.17, 1.17, 1.169, 1.169, 1.168, 
        1.168, 1.167, 1.167, 1.167, 1.166, 1.166, 1.165, 1.165, 1.165, 1.164, 
        1.164, 1.163, 1.163, 1.163, 1.162, 1.162, 1.161, 1.161, 1.16, 1.16, 
        1.16, 1.159, 1.159, 1.158, 1.158, 1.158, 1.157, 1.157, 1.156, 1.156, 
        1.156, 1.155, 1.155, 1.154, 1.154, 1.153, 1.153, 1.153, 1.152, 1.152, 
        1.151, 1.151, 1.151, 1.15, 1.15, 1.149, 1.149, 1.149, 1.148, 1.148, 
        1.147, 1.147, 1.146, 1.146, 1.146, 1.145, 1.145, 1.144, 1.144, 1.144, 
        1.143, 1.143, 1.142, 1.142, 1.142, 1.141, 1.141, 1.14, 1.14, 1.139, 
        1.139, 1.139, 1.138, 1.138, 1.137, 1.137, 1.137, 1.136, 1.136, 1.135, 
        1.135, 1.135, 1.134, 1.134, 1.133, 1.133, 1.133, 1.132, 1.132, 1.131, 
        1.131, 1.13, 1.13, 1.13, 1.129, 1.129, 1.128, 1.128, 1.128, 1.127, 
        1.127, 1.126, 1.126, 1.126, 1.125, 1.125, 1.124, 1.124, 1.124, 1.123, 
        1.123, 1.122, 1.122, 1.121, 1.121, 1.121, 1.12, 1.12, 1.119, 1.119, 
        1.119, 1.118, 1.118, 1.117, 1.117, 1.117, 1.116, 1.116, 1.115, 1.115, 
        1.115, 1.114, 1.114, 1.113, 1.113, 1.113, 1.112, 1.112, 1.111, 1.111, 
        1.11, 1.11, 1.11, 1.109, 1.109, 1.108, 1.108, 1.108, 1.107, 1.107, 
        1.106, 1.106, 1.106, 1.105, 1.105, 1.104, 1.104, 1.104, 1.103, 1.103, 
        1.102, 1.102, 1.102, 1.101, 1.101, 1.1, 1.1, 1.099, 1.099, 1.099, 
        1.098, 1.098, 1.097, 1.097, 1.097, 1.096, 1.096, 1.095, 1.095, 1.095, 
        1.094, 1.094, 1.093, 1.093, 1.093, 1.092, 1.092, 1.091, 1.091, 1.091, 
        1.09, 1.09, 1.089, 1.089, 1.089, 1.088, 1.088, 1.087, 1.087, 1.086, 
        1.086, 1.086, 1.085, 1.085, 1.084, 1.084, 1.084, 1.083, 1.083, 1.082, 
        1.082, 1.082, 1.081, 1.081, 1.08, 1.08, 1.08, 1.079, 1.079, 1.078, 
        1.078, 1.078, 1.077, 1.077, 1.076, 1.076, 1.076, 1.075, 1.075, 1.074, 
        1.074, 1.074, 1.073, 1.073, 1.072, 1.072, 1.072, 1.071, 1.071, 1.07, 
        1.07, 1.069, 1.069, 1.069, 1.068, 1.068, 1.067, 1.067, 1.067, 1.066, 
        1.066, 1.065, 1.065, 1.065, 1.064, 1.064, 1.063, 1.063, 1.063, 1.062, 
        1.062, 1.061, 1.061, 1.061, 1.06, 1.06, 1.059, 1.059, 1.059, 1.058, 
        1.058, 1.057, 1.057, 1.057, 1.056, 1.056, 1.055, 1.055, 1.055, 1.054, 
        1.054, 1.053, 1.053, 1.053, 1.052, 1.052, 1.051, 1.051, 1.05, 1.05, 
        1.05, 1.049, 1.049, 1.048, 1.048, 1.048, 1.047, 1.047, 1.046, 1.046, 
        1.046, 1.045, 1.045, 1.044, 1.044, 1.044, 1.043, 1.043, 1.042, 1.042, 
        1.042, 1.041, 1.041, 1.04, 1.04, 1.04, 1.039, 1.039, 1.038, 1.038, 
        1.038, 1.037, 1.037, 1.036, 1.036, 1.036, 1.035, 1.035, 1.034, 1.034, 
        1.034, 1.033, 1.033, 1.032, 1.032, 1.032, 1.031, 1.031, 1.03, 1.03, 
        1.03, 1.029, 1.029, 1.028, 1.028, 1.028, 1.027, 1.027, 1.026, 1.026, 
        1.026, 1.025, 1.025, 1.024, 1.024, 1.023, 1.023, 1.023, 1.022, 1.022, 
        1.021, 1.021, 1.021, 1.02, 1.02, 1.019, 1.019, 1.019, 1.018, 1.018, 
        1.017, 1.017, 1.017, 1.016, 1.016, 1.015, 1.015, 1.015, 1.014, 1.014, 
        1.013, 1.013, 1.013, 1.012, 1.012, 1.011, 1.011, 1.011, 1.01, 1.01, 
        1.009, 1.009, 1.009, 1.008, 1.008, 1.007, 1.007, 1.007, 1.006, 1.006, 
        1.005, 1.005, 1.005, 1.004, 1.004, 1.003, 1.003, 1.003, 1.002, 1.002, 
        1.001, 1.001, 1.001, 1, 0.9997, 0.9993, 0.9989, 0.9985, 0.9981, 0.9977, 
        0.9973, 0.9969, 0.9965, 0.9961, 0.9957, 0.9953, 0.9949, 0.9945, 0.9941, 0.9937, 
        0.9933, 0.9929, 0.9925, 0.9921, 0.9917, 0.9913, 0.9909, 0.9905, 0.9901, 0.9897, 
        0.9893, 0.9889, 0.9885, 0.9881, 0.9877, 0.9873, 0.9869, 0.9865, 0.9861, 0.9856, 
        0.9852, 0.9848, 0.9844, 0.984, 0.9836, 0.9832, 0.9828, 0.9824, 0.982, 0.9816, 
        0.9812, 0.9808, 0.9804, 0.98, 0.9796, 0.9792, 0.9788, 0.9784, 0.978, 0.9776, 
        0.9772, 0.9768, 0.9764, 0.976, 0.9756, 0.9752, 0.9748, 0.9744, 0.974, 0.9736, 
        0.9732, 0.9728, 0.9724, 0.972, 0.9716, 0.9712, 0.9707, 0.9703, 0.9699, 0.9695, 
        0.9691, 0.9687, 0.9683, 0.9679, 0.9675, 0.9671, 0.9667, 0.9663, 0.9659, 0.9655, 
        0.9651, 0.9647, 0.9643, 0.9639, 0.9635, 0.9631, 0.9627, 0.9623, 0.9619, 0.9615, 
        0.9611, 0.9607, 0.9603, 0.9599, 0.9595, 0.9591, 0.9587, 0.9583, 0.9579, 0.9574, 
        0.957, 0.9566, 0.9562, 0.9558, 0.9554, 0.955, 0.9546, 0.9542, 0.9538, 0.9534, 
        0.953, 0.9526, 0.9522, 0.9518, 0.9514, 0.951, 0.9506, 0.9502, 0.9498, 0.9494, 
        0.949, 0.9486, 0.9482, 0.9478, 0.9474, 0.947, 0.9466, 0.9462, 0.9457, 0.9453, 
        0.9449, 0.9445, 0.9441, 0.9437, 0.9433, 0.9429, 0.9425, 0.9421, 0.9417, 0.9413, 
        0.9409, 0.9405, 0.9401, 0.9397, 0.9393, 0.9389, 0.9385, 0.9381, 0.9377, 0.9373, 
        0.9369, 0.9365, 0.9361, 0.9356, 0.9352, 0.9348, 0.9344, 0.934, 0.9336, 0.9332, 
        0.9328, 0.9324, 0.932, 0.9316, 0.9312, 0.9308, 0.9304, 0.93, 0.9296, 0.9292, 
        0.9288, 0.9284, 0.928, 0.9276, 0.9272, 0.9267, 0.9263, 0.9259, 0.9255, 0.9251, 
        0.9247, 0.9243, 0.9239, 0.9235, 0.9231, 0.9227, 0.9223, 0.9219, 0.9215, 0.9211, 
        0.9207, 0.9203, 0.9199, 0.9195, 0.9191, 0.9186, 0.9182, 0.9178, 0.9174, 0.917, 
        0.9166, 0.9162, 0.9158, 0.9154, 0.915, 0.9146, 0.9142, 0.9138, 0.9134, 0.913, 
        0.9126, 0.9122, 0.9118, 0.9113, 0.9109, 0.9105, 0.9101, 0.9097, 0.9093, 0.9089, 
        0.9085, 0.9081, 0.9077, 0.9073, 0.9069, 0.9065, 0.9061, 0.9057, 0.9053, 0.9049, 
        0.9044, 0.904, 0.9036, 0.9032, 0.9028, 0.9024, 0.902, 0.9016, 0.9012, 0.9008, 
        0.9004, 0.9, 0.8996, 0.8992, 0.8988, 0.8983, 0.8979, 0.8975, 0.8971, 0.8967, 
        0.8963, 0.8959, 0.8955, 0.8951, 0.8947, 0.8943, 0.8939, 0.8935, 0.8931, 0.8926, 
        0.8922, 0.8918, 0.8914, 0.891, 0.8906, 0.8902, 0.8898, 0.8894, 0.889, 0.8886, 
        0.8882, 0.8878, 0.8873, 0.8869, 0.8865, 0.8861, 0.8857, 0.8853, 0.8849, 0.8845, 
        0.8841, 0.8837, 0.8833, 0.8829, 0.8825, 0.882, 0.8816, 0.8812, 0.8808, 0.8804, 
        0.88, 0.8796, 0.8792, 0.8788, 0.8784, 0.878, 0.8775, 0.8771, 0.8767, 0.8763, 
        0.8759, 0.8755, 0.8751, 0.8747, 0.8743, 0.8739, 0.8735, 0.873, 0.8726, 0.8722, 
        0.8718, 0.8714, 0.871, 0.8706, 0.8702, 0.8698, 0.8694, 0.869, 0.8685, 0.8681, 
        0.8677, 0.8673, 0.8669, 0.8665, 0.8661, 0.8657, 0.8653, 0.8649, 0.8644, 0.864, 
        0.8636, 0.8632, 0.8628, 0.8624, 0.862, 0.8616, 0.8612, 0.8607, 0.8603, 0.8599, 
        0.8595, 0.8591, 0.8587, 0.8583, 0.8579, 0.8575, 0.857, 0.8566, 0.8562, 0.8558, 
        0.8554, 0.855, 0.8546, 0.8542, 0.8538, 0.8533, 0.8529, 0.8525, 0.8521, 0.8517, 
        0.8513, 0.8509, 0.8505, 0.85, 0.8496, 0.8492, 0.8488, 0.8484, 0.848, 0.8476, 
        0.8472, 0.8467, 0.8463, 0.8459, 0.8455, 0.8451, 0.8447, 0.8443, 0.8439, 0.8434, 
        0.843, 0.8426, 0.8422, 0.8418, 0.8414, 0.841, 0.8406, 0.8401, 0.8397, 0.8393, 
        0.8389, 0.8385, 0.8381, 0.8377, 0.8372, 0.8368, 0.8364, 0.836, 0.8356, 0.8352, 
        0.8348, 0.8343, 0.8339, 0.8335, 0.8331, 0.8327, 0.8323, 0.8319, 0.8314, 0.831, 
        0.8306, 0.8302, 0.8298, 0.8294, 0.8289, 0.8285, 0.8281, 0.8277, 0.8273, 0.8269, 
        0.8265, 0.826, 0.8256, 0.8252, 0.8248, 0.8244, 0.824, 0.8235, 0.8231, 0.8227, 
        0.8223, 0.8219, 0.8215, 0.821, 0.8206, 0.8202, 0.8198, 0.8194, 0.819, 0.8185, 
        0.8181, 0.8177, 0.8173, 0.8169, 0.8165, 0.816, 0.8156, 0.8152, 0.8148, 0.8144, 
        0.814, 0.8135, 0.8131, 0.8127, 0.8123, 0.8119, 0.8114, 0.811, 0.8106, 0.8102, 
        0.8098, 0.8094, 0.8089, 0.8085, 0.8081, 0.8077, 0.8073, 0.8068, 0.8064, 0.806, 
        0.8056, 0.8052, 0.8047, 0.8043, 0.8039, 0.8035, 0.8031, 0.8026, 0.8022, 0.8018, 
        0.8014, 0.801, 0.8005, 0.8001, 0.7997, 0.7993, 0.7989, 0.7984, 0.798, 0.7976, 
        0.7972, 0.7968, 0.7963, 0.7959, 0.7955, 0.7951, 0.7947, 0.7942, 0.7938, 0.7934, 
        0.793, 0.7926, 0.7921, 0.7917, 0.7913, 0.7909, 0.7904, 0.79, 0.7896, 0.7892, 
        0.7888, 0.7883, 0.7879, 0.7875, 0.7871, 0.7866, 0.7862, 0.7858, 0.7854, 0.7849, 
        0.7845, 0.7841, 0.7837, 0.7833, 0.7828, 0.7824, 0.782, 0.7816, 0.7811, 0.7807, 
        0.7803, 0.7799, 0.7794, 0.779, 0.7786, 0.7782, 0.7777, 0.7773, 0.7769, 0.7765, 
        0.776, 0.7756, 0.7752, 0.7748, 0.7743, 0.7739, 0.7735, 0.7731, 0.7726, 0.7722, 
        0.7718, 0.7714, 0.7709, 0.7705, 0.7701, 0.7697, 0.7692, 0.7688, 0.7684, 0.7679, 
        0.7675, 0.7671, 0.7667, 0.7662, 0.7658, 0.7654, 0.765, 0.7645, 0.7641, 0.7637, 
        0.7632, 0.7628, 0.7624, 0.762, 0.7615, 0.7611, 0.7607, 0.7602, 0.7598, 0.7594, 
        0.759, 0.7585, 0.7581, 0.7577, 0.7572, 0.7568, 0.7564, 0.756, 0.7555, 0.7551, 
        0.7547, 0.7542, 0.7538, 0.7534, 0.7529, 0.7525, 0.7521, 0.7516, 0.7512, 0.7508, 
        0.7504, 0.7499, 0.7495, 0.7491, 0.7486, 0.7482, 0.7478, 0.7473, 0.7469, 0.7465, 
        0.746, 0.7456, 0.7452, 0.7447, 0.7443, 0.7439, 0.7434, 0.743, 0.7426, 0.7421, 
        0.7417, 0.7413, 0.7408, 0.7404, 0.74, 0.7395, 0.7391, 0.7387, 0.7382, 0.7378, 
        0.7374, 0.7369, 0.7365, 0.7361, 0.7356, 0.7352, 0.7348, 0.7343, 0.7339, 0.7335, 
        0.733, 0.7326, 0.7321, 0.7317, 0.7313, 0.7308, 0.7304, 0.73, 0.7295, 0.7291, 
        0.7287, 0.7282, 0.7278, 0.7273, 0.7269, 0.7265, 0.726, 0.7256, 0.7252, 0.7247, 
        0.7243, 0.7238, 0.7234, 0.723, 0.7225, 0.7221, 0.7216, 0.7212, 0.7208, 0.7203, 
        0.7199, 0.7195, 0.719, 0.7186, 0.7181, 0.7177, 0.7173, 0.7168, 0.7164, 0.7159, 
        0.7155, 0.7151, 0.7146, 0.7142, 0.7137, 0.7133, 0.7128, 0.7124, 0.712, 0.7115, 
        0.7111, 0.7106, 0.7102, 0.7098, 0.7093, 0.7089, 0.7084, 0.708, 0.7075, 0.7071, 
        0.7066, 0.7062, 0.7058, 0.7053, 0.7049, 0.7044, 0.704, 0.7035, 0.7031, 0.7027, 
        0.7022, 0.7018, 0.7013, 0.7009, 0.7004, 0.7, 0.6995, 0.6991, 0.6986, 0.6982, 
        0.6978, 0.6973, 0.6969, 0.6964, 0.696, 0.6955, 0.6951, 0.6946, 0.6942, 0.6937, 
        0.6933, 0.6928, 0.6924, 0.6919, 0.6915, 0.691, 0.6906, 0.6901, 0.6897, 0.6892, 
        0.6888, 0.6883, 0.6879, 0.6874, 0.687, 0.6865, 0.6861, 0.6856, 0.6852, 0.6847, 
        0.6843, 0.6838, 0.6834, 0.6829, 0.6825, 0.682, 0.6816, 0.6811, 0.6807, 0.6802, 
        0.6798, 0.6793, 0.6789, 0.6784, 0.678, 0.6775, 0.6771, 0.6766, 0.6762, 0.6757, 
        0.6752, 0.6748, 0.6743, 0.6739, 0.6734, 0.673, 0.6725, 0.6721, 0.6716, 0.6711, 
        0.6707, 0.6702, 0.6698, 0.6693, 0.6689, 0.6684, 0.668, 0.6675, 0.667, 0.6666, 
        0.6661, 0.6657, 0.6652, 0.6648, 0.6643, 0.6638, 0.6634, 0.6629, 0.6625, 0.662, 
        0.6615, 0.6611, 0.6606, 0.6602, 0.6597, 0.6592, 0.6588, 0.6583, 0.6579, 0.6574, 
        0.6569, 0.6565, 0.656, 0.6556, 0.6551, 0.6546, 0.6542, 0.6537, 0.6532, 0.6528, 
        0.6523, 0.6519, 0.6514, 0.6509, 0.6505, 0.65, 0.6495, 0.6491, 0.6486, 0.6481, 
        0.6477, 0.6472, 0.6468, 0.6463, 0.6458, 0.6454, 0.6449, 0.6444, 0.644, 0.6435, 
        0.643, 0.6426, 0.6421, 0.6416, 0.6412, 0.6407, 0.6402, 0.6397, 0.6393, 0.6388, 
        0.6383, 0.6379, 0.6374, 0.6369, 0.6365, 0.636, 0.6355, 0.6351, 0.6346, 0.6341, 
        0.6336, 0.6332, 0.6327, 0.6322, 0.6318, 0.6313, 0.6308, 0.6303, 0.6299, 0.6294, 
        0.6289, 0.6285, 0.628, 0.6275, 0.627, 0.6266, 0.6261, 0.6256, 0.6251, 0.6247, 
        0.6242, 0.6237, 0.6232, 0.6228, 0.6223, 0.6218, 0.6213, 0.6208, 0.6204, 0.6199, 
        0.6194, 0.6189, 0.6185, 0.618, 0.6175, 0.617, 0.6165, 0.6161, 0.6156, 0.6151, 
        0.6146, 0.6142, 0.6137, 0.6132, 0.6127, 0.6122, 0.6117, 0.6113, 0.6108, 0.6103, 
        0.6098, 0.6093, 0.6089, 0.6084, 0.6079, 0.6074, 0.6069, 0.6064, 0.606, 0.6055, 
        0.605, 0.6045, 0.604, 0.6035, 0.603, 0.6026, 0.6021, 0.6016, 0.6011, 0.6006, 
        0.6001, 0.5996, 0.5992, 0.5987, 0.5982, 0.5977, 0.5972, 0.5967, 0.5962, 0.5957, 
        0.5952, 0.5948, 0.5943, 0.5938, 0.5933, 0.5928, 0.5923, 0.5918, 0.5913, 0.5908, 
        0.5903, 0.5898, 0.5894, 0.5889, 0.5884, 0.5879, 0.5874, 0.5869, 0.5864, 0.5859, 
        0.5854, 0.5849, 0.5844, 0.5839, 0.5834, 0.5829, 0.5824, 0.5819, 0.5814, 0.5809, 
        0.5804, 0.5799, 0.5794, 0.5789, 0.5784, 0.5779, 0.5774, 0.5769, 0.5764, 0.5759, 
        0.5754, 0.5749, 0.5744, 0.5739, 0.5734, 0.5729, 0.5724, 0.5719, 0.5714, 0.5709, 
        0.5704, 0.5699, 0.5694, 0.5689, 0.5684, 0.5679, 0.5674, 0.5669, 0.5664, 0.5659, 
        0.5654, 0.5649, 0.5644, 0.5639, 0.5633, 0.5628, 0.5623, 0.5618, 0.5613, 0.5608, 
        0.5603, 0.5598, 0.5593, 0.5588, 0.5582, 0.5577, 0.5572, 0.5567, 0.5562, 0.5557, 
        0.5552, 0.5547, 0.5541, 0.5536, 0.5531, 0.5526, 0.5521, 0.5516, 0.5511, 0.5505, 
        0.55, 0.5495, 0.549, 0.5485, 0.548, 0.5474, 0.5469, 0.5464, 0.5459, 0.5454, 
        0.5448, 0.5443, 0.5438, 0.5433, 0.5428, 0.5422, 0.5417, 0.5412, 0.5407, 0.5402, 
        0.5396, 0.5391, 0.5386, 0.5381, 0.5375, 0.537, 0.5365, 0.536, 0.5354, 0.5349, 
        0.5344, 0.5339, 0.5333, 0.5328, 0.5323, 0.5317, 0.5312, 0.5307, 0.5302, 0.5296, 
        0.5291, 0.5286, 0.528, 0.5275, 0.527, 0.5264, 0.5259, 0.5254, 0.5248, 0.5243, 
        0.5238, 0.5232, 0.5227, 0.5222, 0.5216, 0.5211, 0.5206, 0.52, 0.5195, 0.5189, 
        0.5184, 0.5179, 0.5173, 0.5168, 0.5162, 0.5157, 0.5152, 0.5146, 0.5141, 0.5135, 
        0.513, 0.5124, 0.5119, 0.5114, 0.5108, 0.5103, 0.5097, 0.5092, 0.5086, 0.5081, 
        0.5075, 0.507, 0.5064, 0.5059, 0.5053, 0.5048, 0.5043, 0.5037, 0.5032, 0.5026, 
        0.502, 0.5015, 0.5009, 0.5004, 0.4998, 0.4993, 0.4987, 0.4982, 0.4976, 0.4971, 
        0.4965, 0.496, 0.4954, 0.4948, 0.4943, 0.4937, 0.4932, 0.4926, 0.492, 0.4915, 
        0.4909, 0.4904, 0.4898, 0.4892, 0.4887, 0.4881, 0.4875, 0.487, 0.4864, 0.4859, 
        0.4853, 0.4847, 0.4842, 0.4836, 0.483, 0.4825, 0.4819, 0.4813, 0.4807, 0.4802, 
        0.4796, 0.479, 0.4785, 0.4779, 0.4773, 0.4767, 0.4762, 0.4756, 0.475, 0.4744, 
        0.4739, 0.4733, 0.4727, 0.4721, 0.4716, 0.471, 0.4704, 0.4698, 0.4692, 0.4687, 
        0.4681, 0.4675, 0.4669, 0.4663, 0.4657, 0.4652, 0.4646, 0.464, 0.4634, 0.4628, 
        0.4622, 0.4616, 0.461, 0.4605, 0.4599, 0.4593, 0.4587, 0.4581, 0.4575, 0.4569, 
        0.4563, 0.4557, 0.4551, 0.4545, 0.4539, 0.4533, 0.4527, 0.4521, 0.4515, 0.451, 
        0.4504, 0.4498, 0.4491, 0.4485, 0.4479, 0.4473, 0.4467, 0.4461, 0.4455, 0.4449, 
        0.4443, 0.4437, 0.4431, 0.4425, 0.4419, 0.4413, 0.4407, 0.4401, 0.4394, 0.4388, 
        0.4382, 0.4376, 0.437, 0.4364, 0.4358, 0.4351, 0.4345, 0.4339, 0.4333, 0.4327, 
        0.4321, 0.4314, 0.4308, 0.4302, 0.4296, 0.4289, 0.4283, 0.4277, 0.4271, 0.4264, 
        0.4258, 0.4252, 0.4246, 0.4239, 0.4233, 0.4227, 0.422, 0.4214, 0.4208, 0.4201, 
        0.4195, 0.4189, 0.4182, 0.4176, 0.4169, 0.4163, 0.4157, 0.415, 0.4144, 0.4137, 
        0.4131, 0.4125, 0.4118, 0.4112, 0.4105, 0.4099, 0.4092, 0.4086, 0.4079, 0.4073, 
        0.4066, 0.406, 0.4053, 0.4047, 0.404, 0.4034, 0.4027, 0.402, 0.4014, 0.4007, 
        0.4001, 0.3994, 0.3987, 0.3981, 0.3974, 0.3967, 0.3961, 0.3954, 0.3947, 0.3941, 
        0.3934, 0.3927, 0.3921, 0.3914, 0.3907, 0.39, 0.3894, 0.3887, 0.388, 0.3873, 
        0.3866, 0.386, 0.3853, 0.3846, 0.3839, 0.3832, 0.3825, 0.3819, 0.3812, 0.3805, 
        0.3798, 0.3791, 0.3784, 0.3777, 0.377, 0.3763, 0.3756, 0.3749, 0.3742, 0.3735, 
        0.3728, 0.3721, 0.3714, 0.3707, 0.37, 0.3693, 0.3686, 0.3679, 0.3672, 0.3665, 
        0.3657, 0.365, 0.3643, 0.3636, 0.3629, 0.3622, 0.3614, 0.3607, 0.36, 0.3593, 
        0.3585, 0.3578, 0.3571, 0.3564, 0.3556, 0.3549, 0.3542, 0.3534, 0.3527, 0.352, 
        0.3512, 0.3505, 0.3497, 0.349, 0.3483, 0.3475, 0.3468, 0.346, 0.3453, 0.3445, 
        0.3438, 0.343, 0.3422, 0.3415, 0.3407, 0.34, 0.3392, 0.3384, 0.3377, 0.3369, 
        0.3361, 0.3354, 0.3346, 0.3338, 0.3331, 0.3323, 0.3315, 0.3307, 0.3299, 0.3292, 
        0.3284, 0.3276, 0.3268, 0.326, 0.3252, 0.3244, 0.3236, 0.3228, 0.3221, 0.3213, 
        0.3205, 0.3196, 0.3188, 0.318, 0.3172, 0.3164, 0.3156, 0.3148, 0.314, 0.3132, 
        0.3123, 0.3115, 0.3107, 0.3099, 0.309, 0.3082, 0.3074, 0.3065, 0.3057, 0.3049, 
        0.304, 0.3032, 0.3023, 0.3015, 0.3007, 0.2998, 0.2989, 0.2981, 0.2972, 0.2964, 
        0.2955, 0.2946, 0.2938, 0.2929, 0.292, 0.2912, 0.2903, 0.2894, 0.2885, 0.2877, 
        0.2868, 0.2859, 0.285, 0.2841, 0.2832, 0.2823, 0.2814, 0.2805, 0.2796, 0.2787, 
        0.2778, 0.2768, 0.2759, 0.275, 0.2741, 0.2732, 0.2722, 0.2713, 0.2704, 0.2694, 
        0.2685, 0.2675, 0.2666, 0.2656, 0.2647, 0.2637, 0.2628, 0.2618, 0.2608, 0.2599, 
        0.2589, 0.2579, 0.2569, 0.256, 0.255, 0.254, 0.253, 0.252, 0.251, 0.25, 
        0.249, 0.248, 0.2469, 0.2459, 0.2449, 0.2439, 0.2428, 0.2418, 0.2408, 0.2397, 
        0.2387, 0.2376, 0.2365, 0.2355, 0.2344, 0.2333, 0.2323, 0.2312, 0.2301, 0.229, 
        0.2279, 0.2268, 0.2257, 0.2246, 0.2235, 0.2223, 0.2212, 0.2201, 0.2189, 0.2178, 
        0.2166, 0.2155, 0.2143, 0.2132, 0.212, 0.2108, 0.2096, 0.2084, 0.2072, 0.206, 
        0.2048, 0.2036, 0.2023, 0.2011, 0.1999, 0.1986, 0.1974, 0.1961, 0.1948, 0.1935, 
        0.1923, 0.191, 0.1896, 0.1883, 0.187, 0.1857, 0.1843, 0.183, 0.1816, 0.1802, 
        0.1789, 0.1775, 0.1761, 0.1747, 0.1732, 0.1718, 0.1703, 0.1689, 0.1674, 0.1659, 
        0.1644, 0.1629, 0.1614, 0.1599, 0.1583, 0.1567, 0.1551, 0.1535, 0.1519, 0.1503, 
        0.1486, 0.147, 0.1453, 0.1436, 0.1418, 0.1401, 0.1383, 0.1365, 0.1347, 0.1329, 
        0.131, 0.1291, 0.1272, 0.1252, 0.1233, 0.1213, 0.1192, 0.1171, 0.115, 0.1129, 
        0.1107, 0.1084, 0.1061, 0.1038, 0.1014, 0.09894, 0.09643, 0.09385, 0.0912, 0.08847, 
        0.08566, 0.08275, 0.07974, 0.0766, 0.07334, 0.06992, 0.06633, 0.06253, 0.05849, 0.05415, 
        0.04943, 0.0442, 0.03828, 0.03125, 0.0221, -0};

        const static double cosvals[max] = { 
        1, 1, 1, 1, 1, 1, 0.9999, 0.9999, 0.9999, 0.9999, 
        0.9999, 0.9998, 0.9998, 0.9998, 0.9997, 0.9997, 0.9997, 0.9996, 0.9996, 0.9995, 
        0.9995, 0.9994, 0.9994, 0.9993, 0.9993, 0.9992, 0.9991, 0.9991, 0.999, 0.9989, 
        0.9989, 0.9988, 0.9987, 0.9986, 0.9986, 0.9985, 0.9984, 0.9983, 0.9982, 0.9981, 
        0.998, 0.9979, 0.9978, 0.9977, 0.9976, 0.9975, 0.9974, 0.9973, 0.9972, 0.9971, 
        0.9969, 0.9968, 0.9967, 0.9966, 0.9964, 0.9963, 0.9962, 0.996, 0.9959, 0.9958, 
        0.9956, 0.9955, 0.9953, 0.9952, 0.995, 0.9949, 0.9947, 0.9946, 0.9944, 0.9942, 
        0.9941, 0.9939, 0.9937, 0.9936, 0.9934, 0.9932, 0.993, 0.9929, 0.9927, 0.9925, 
        0.9923, 0.9921, 0.9919, 0.9917, 0.9915, 0.9913, 0.9911, 0.9909, 0.9907, 0.9905, 
        0.9903, 0.9901, 0.9898, 0.9896, 0.9894, 0.9892, 0.989, 0.9887, 0.9885, 0.9883, 
        0.988, 0.9878, 0.9875, 0.9873, 0.9871, 0.9868, 0.9866, 0.9863, 0.9861, 0.9858, 
        0.9855, 0.9853, 0.985, 0.9847, 0.9845, 0.9842, 0.9839, 0.9837, 0.9834, 0.9831, 
        0.9828, 0.9825, 0.9823, 0.982, 0.9817, 0.9814, 0.9811, 0.9808, 0.9805, 0.9802, 
        0.9799, 0.9796, 0.9793, 0.9789, 0.9786, 0.9783, 0.978, 0.9777, 0.9774, 0.977, 
        0.9767, 0.9764, 0.976, 0.9757, 0.9754, 0.975, 0.9747, 0.9743, 0.974, 0.9736, 
        0.9733, 0.9729, 0.9726, 0.9722, 0.9719, 0.9715, 0.9711, 0.9708, 0.9704, 0.97, 
        0.9697, 0.9693, 0.9689, 0.9685, 0.9681, 0.9678, 0.9674, 0.967, 0.9666, 0.9662, 
        0.9658, 0.9654, 0.965, 0.9646, 0.9642, 0.9638, 0.9634, 0.963, 0.9625, 0.9621, 
        0.9617, 0.9613, 0.9609, 0.9604, 0.96, 0.9596, 0.9591, 0.9587, 0.9583, 0.9578, 
        0.9574, 0.9569, 0.9565, 0.956, 0.9556, 0.9551, 0.9547, 0.9542, 0.9538, 0.9533, 
        0.9528, 0.9524, 0.9519, 0.9514, 0.951, 0.9505, 0.95, 0.9495, 0.949, 0.9486, 
        0.9481, 0.9476, 0.9471, 0.9466, 0.9461, 0.9456, 0.9451, 0.9446, 0.9441, 0.9436, 
        0.9431, 0.9426, 0.9421, 0.9415, 0.941, 0.9405, 0.94, 0.9395, 0.9389, 0.9384, 
        0.9379, 0.9373, 0.9368, 0.9363, 0.9357, 0.9352, 0.9346, 0.9341, 0.9335, 0.933, 
        0.9324, 0.9319, 0.9313, 0.9308, 0.9302, 0.9296, 0.9291, 0.9285, 0.9279, 0.9274, 
        0.9268, 0.9262, 0.9256, 0.925, 0.9245, 0.9239, 0.9233, 0.9227, 0.9221, 0.9215, 
        0.9209, 0.9203, 0.9197, 0.9191, 0.9185, 0.9179, 0.9173, 0.9167, 0.9161, 0.9154, 
        0.9148, 0.9142, 0.9136, 0.913, 0.9123, 0.9117, 0.9111, 0.9104, 0.9098, 0.9092, 
        0.9085, 0.9079, 0.9072, 0.9066, 0.9059, 0.9053, 0.9046, 0.904, 0.9033, 0.9027, 
        0.902, 0.9013, 0.9007, 0.9, 0.8993, 0.8987, 0.898, 0.8973, 0.8966, 0.896, 
        0.8953, 0.8946, 0.8939, 0.8932, 0.8925, 0.8918, 0.8911, 0.8904, 0.8897, 0.889, 
        0.8883, 0.8876, 0.8869, 0.8862, 0.8855, 0.8848, 0.8841, 0.8834, 0.8826, 0.8819, 
        0.8812, 0.8805, 0.8797, 0.879, 0.8783, 0.8775, 0.8768, 0.8761, 0.8753, 0.8746, 
        0.8738, 0.8731, 0.8723, 0.8716, 0.8708, 0.8701, 0.8693, 0.8686, 0.8678, 0.867, 
        0.8663, 0.8655, 0.8647, 0.864, 0.8632, 0.8624, 0.8616, 0.8609, 0.8601, 0.8593, 
        0.8585, 0.8577, 0.8569, 0.8561, 0.8554, 0.8546, 0.8538, 0.853, 0.8522, 0.8514, 
        0.8505, 0.8497, 0.8489, 0.8481, 0.8473, 0.8465, 0.8457, 0.8449, 0.844, 0.8432, 
        0.8424, 0.8416, 0.8407, 0.8399, 0.8391, 0.8382, 0.8374, 0.8365, 0.8357, 0.8349, 
        0.834, 0.8332, 0.8323, 0.8315, 0.8306, 0.8298, 0.8289, 0.828, 0.8272, 0.8263, 
        0.8255, 0.8246, 0.8237, 0.8228, 0.822, 0.8211, 0.8202, 0.8193, 0.8185, 0.8176, 
        0.8167, 0.8158, 0.8149, 0.814, 0.8131, 0.8123, 0.8114, 0.8105, 0.8096, 0.8087, 
        0.8078, 0.8068, 0.8059, 0.805, 0.8041, 0.8032, 0.8023, 0.8014, 0.8005, 0.7995, 
        0.7986, 0.7977, 0.7968, 0.7958, 0.7949, 0.794, 0.793, 0.7921, 0.7912, 0.7902, 
        0.7893, 0.7883, 0.7874, 0.7865, 0.7855, 0.7846, 0.7836, 0.7827, 0.7817, 0.7807, 
        0.7798, 0.7788, 0.7779, 0.7769, 0.7759, 0.775, 0.774, 0.773, 0.772, 0.7711, 
        0.7701, 0.7691, 0.7681, 0.7671, 0.7662, 0.7652, 0.7642, 0.7632, 0.7622, 0.7612, 
        0.7602, 0.7592, 0.7582, 0.7572, 0.7562, 0.7552, 0.7542, 0.7532, 0.7522, 0.7512, 
        0.7502, 0.7491, 0.7481, 0.7471, 0.7461, 0.7451, 0.744, 0.743, 0.742, 0.741, 
        0.7399, 0.7389, 0.7379, 0.7368, 0.7358, 0.7347, 0.7337, 0.7327, 0.7316, 0.7306, 
        0.7295, 0.7285, 0.7274, 0.7264, 0.7253, 0.7242, 0.7232, 0.7221, 0.7211, 0.72, 
        0.7189, 0.7179, 0.7168, 0.7157, 0.7147, 0.7136, 0.7125, 0.7114, 0.7104, 0.7093, 
        0.7082, 0.7071, 0.706, 0.7049, 0.7038, 0.7028, 0.7017, 0.7006, 0.6995, 0.6984, 
        0.6973, 0.6962, 0.6951, 0.694, 0.6929, 0.6918, 0.6907, 0.6895, 0.6884, 0.6873, 
        0.6862, 0.6851, 0.684, 0.6828, 0.6817, 0.6806, 0.6795, 0.6784, 0.6772, 0.6761, 
        0.675, 0.6738, 0.6727, 0.6716, 0.6704, 0.6693, 0.6681, 0.667, 0.6659, 0.6647, 
        0.6636, 0.6624, 0.6613, 0.6601, 0.659, 0.6578, 0.6567, 0.6555, 0.6543, 0.6532, 
        0.652, 0.6508, 0.6497, 0.6485, 0.6473, 0.6462, 0.645, 0.6438, 0.6427, 0.6415, 
        0.6403, 0.6391, 0.6379, 0.6368, 0.6356, 0.6344, 0.6332, 0.632, 0.6308, 0.6296, 
        0.6284, 0.6273, 0.6261, 0.6249, 0.6237, 0.6225, 0.6213, 0.6201, 0.6189, 0.6176, 
        0.6164, 0.6152, 0.614, 0.6128, 0.6116, 0.6104, 0.6092, 0.6079, 0.6067, 0.6055, 
        0.6043, 0.6031, 0.6018, 0.6006, 0.5994, 0.5982, 0.5969, 0.5957, 0.5945, 0.5932, 
        0.592, 0.5908, 0.5895, 0.5883, 0.587, 0.5858, 0.5846, 0.5833, 0.5821, 0.5808, 
        0.5796, 0.5783, 0.5771, 0.5758, 0.5746, 0.5733, 0.572, 0.5708, 0.5695, 0.5683, 
        0.567, 0.5657, 0.5645, 0.5632, 0.5619, 0.5607, 0.5594, 0.5581, 0.5568, 0.5556, 
        0.5543, 0.553, 0.5517, 0.5505, 0.5492, 0.5479, 0.5466, 0.5453, 0.544, 0.5428, 
        0.5415, 0.5402, 0.5389, 0.5376, 0.5363, 0.535, 0.5337, 0.5324, 0.5311, 0.5298, 
        0.5285, 0.5272, 0.5259, 0.5246, 0.5233, 0.522, 0.5207, 0.5194, 0.518, 0.5167, 
        0.5154, 0.5141, 0.5128, 0.5115, 0.5102, 0.5088, 0.5075, 0.5062, 0.5049, 0.5035, 
        0.5022, 0.5009, 0.4996, 0.4982, 0.4969, 0.4956, 0.4942, 0.4929, 0.4916, 0.4902, 
        0.4889, 0.4876, 0.4862, 0.4849, 0.4835, 0.4822, 0.4808, 0.4795, 0.4781, 0.4768, 
        0.4755, 0.4741, 0.4727, 0.4714, 0.47, 0.4687, 0.4673, 0.466, 0.4646, 0.4633, 
        0.4619, 0.4605, 0.4592, 0.4578, 0.4564, 0.4551, 0.4537, 0.4523, 0.451, 0.4496, 
        0.4482, 0.4469, 0.4455, 0.4441, 0.4427, 0.4414, 0.44, 0.4386, 0.4372, 0.4359, 
        0.4345, 0.4331, 0.4317, 0.4303, 0.4289, 0.4276, 0.4262, 0.4248, 0.4234, 0.422, 
        0.4206, 0.4192, 0.4178, 0.4164, 0.415, 0.4136, 0.4122, 0.4108, 0.4094, 0.408, 
        0.4066, 0.4052, 0.4038, 0.4024, 0.401, 0.3996, 0.3982, 0.3968, 0.3954, 0.394, 
        0.3926, 0.3912, 0.3898, 0.3883, 0.3869, 0.3855, 0.3841, 0.3827, 0.3813, 0.3798, 
        0.3784, 0.377, 0.3756, 0.3742, 0.3727, 0.3713, 0.3699, 0.3685, 0.367, 0.3656, 
        0.3642, 0.3628, 0.3613, 0.3599, 0.3585, 0.357, 0.3556, 0.3542, 0.3527, 0.3513, 
        0.3499, 0.3484, 0.347, 0.3455, 0.3441, 0.3427, 0.3412, 0.3398, 0.3383, 0.3369, 
        0.3354, 0.334, 0.3326, 0.3311, 0.3297, 0.3282, 0.3268, 0.3253, 0.3239, 0.3224, 
        0.321, 0.3195, 0.318, 0.3166, 0.3151, 0.3137, 0.3122, 0.3108, 0.3093, 0.3078, 
        0.3064, 0.3049, 0.3035, 0.302, 0.3005, 0.2991, 0.2976, 0.2962, 0.2947, 0.2932, 
        0.2918, 0.2903, 0.2888, 0.2873, 0.2859, 0.2844, 0.2829, 0.2815, 0.28, 0.2785, 
        0.277, 0.2756, 0.2741, 0.2726, 0.2711, 0.2697, 0.2682, 0.2667, 0.2652, 0.2638, 
        0.2623, 0.2608, 0.2593, 0.2578, 0.2563, 0.2549, 0.2534, 0.2519, 0.2504, 0.2489, 
        0.2474, 0.246, 0.2445, 0.243, 0.2415, 0.24, 0.2385, 0.237, 0.2355, 0.234, 
        0.2326, 0.2311, 0.2296, 0.2281, 0.2266, 0.2251, 0.2236, 0.2221, 0.2206, 0.2191, 
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        0.7038, 0.7049, 0.706, 0.7071, 0.7082, 0.7093, 0.7104, 0.7114, 0.7125, 0.7136, 
        0.7147, 0.7157, 0.7168, 0.7179, 0.7189, 0.72, 0.7211, 0.7221, 0.7232, 0.7242, 
        0.7253, 0.7264, 0.7274, 0.7285, 0.7295, 0.7306, 0.7316, 0.7327, 0.7337, 0.7347, 
        0.7358, 0.7368, 0.7379, 0.7389, 0.7399, 0.741, 0.742, 0.743, 0.744, 0.7451, 
        0.7461, 0.7471, 0.7481, 0.7491, 0.7502, 0.7512, 0.7522, 0.7532, 0.7542, 0.7552, 
        0.7562, 0.7572, 0.7582, 0.7592, 0.7602, 0.7612, 0.7622, 0.7632, 0.7642, 0.7652, 
        0.7662, 0.7671, 0.7681, 0.7691, 0.7701, 0.7711, 0.772, 0.773, 0.774, 0.775, 
        0.7759, 0.7769, 0.7779, 0.7788, 0.7798, 0.7807, 0.7817, 0.7827, 0.7836, 0.7846, 
        0.7855, 0.7865, 0.7874, 0.7883, 0.7893, 0.7902, 0.7912, 0.7921, 0.793, 0.794, 
        0.7949, 0.7958, 0.7968, 0.7977, 0.7986, 0.7995, 0.8005, 0.8014, 0.8023, 0.8032, 
        0.8041, 0.805, 0.8059, 0.8068, 0.8078, 0.8087, 0.8096, 0.8105, 0.8114, 0.8123, 
        0.8131, 0.814, 0.8149, 0.8158, 0.8167, 0.8176, 0.8185, 0.8193, 0.8202, 0.8211, 
        0.822, 0.8228, 0.8237, 0.8246, 0.8255, 0.8263, 0.8272, 0.828, 0.8289, 0.8298, 
        0.8306, 0.8315, 0.8323, 0.8332, 0.834, 0.8349, 0.8357, 0.8365, 0.8374, 0.8382, 
        0.8391, 0.8399, 0.8407, 0.8416, 0.8424, 0.8432, 0.844, 0.8449, 0.8457, 0.8465, 
        0.8473, 0.8481, 0.8489, 0.8497, 0.8505, 0.8514, 0.8522, 0.853, 0.8538, 0.8546, 
        0.8554, 0.8561, 0.8569, 0.8577, 0.8585, 0.8593, 0.8601, 0.8609, 0.8616, 0.8624, 
        0.8632, 0.864, 0.8647, 0.8655, 0.8663, 0.867, 0.8678, 0.8686, 0.8693, 0.8701, 
        0.8708, 0.8716, 0.8723, 0.8731, 0.8738, 0.8746, 0.8753, 0.8761, 0.8768, 0.8775, 
        0.8783, 0.879, 0.8797, 0.8805, 0.8812, 0.8819, 0.8826, 0.8834, 0.8841, 0.8848, 
        0.8855, 0.8862, 0.8869, 0.8876, 0.8883, 0.889, 0.8897, 0.8904, 0.8911, 0.8918, 
        0.8925, 0.8932, 0.8939, 0.8946, 0.8953, 0.896, 0.8966, 0.8973, 0.898, 0.8987, 
        0.8993, 0.9, 0.9007, 0.9013, 0.902, 0.9027, 0.9033, 0.904, 0.9046, 0.9053, 
        0.9059, 0.9066, 0.9072, 0.9079, 0.9085, 0.9092, 0.9098, 0.9104, 0.9111, 0.9117, 
        0.9123, 0.913, 0.9136, 0.9142, 0.9148, 0.9154, 0.9161, 0.9167, 0.9173, 0.9179, 
        0.9185, 0.9191, 0.9197, 0.9203, 0.9209, 0.9215, 0.9221, 0.9227, 0.9233, 0.9239, 
        0.9245, 0.925, 0.9256, 0.9262, 0.9268, 0.9274, 0.9279, 0.9285, 0.9291, 0.9296, 
        0.9302, 0.9308, 0.9313, 0.9319, 0.9324, 0.933, 0.9335, 0.9341, 0.9346, 0.9352, 
        0.9357, 0.9363, 0.9368, 0.9373, 0.9379, 0.9384, 0.9389, 0.9395, 0.94, 0.9405, 
        0.941, 0.9415, 0.9421, 0.9426, 0.9431, 0.9436, 0.9441, 0.9446, 0.9451, 0.9456, 
        0.9461, 0.9466, 0.9471, 0.9476, 0.9481, 0.9486, 0.949, 0.9495, 0.95, 0.9505, 
        0.951, 0.9514, 0.9519, 0.9524, 0.9528, 0.9533, 0.9538, 0.9542, 0.9547, 0.9551, 
        0.9556, 0.956, 0.9565, 0.9569, 0.9574, 0.9578, 0.9583, 0.9587, 0.9591, 0.9596, 
        0.96, 0.9604, 0.9609, 0.9613, 0.9617, 0.9621, 0.9625, 0.963, 0.9634, 0.9638, 
        0.9642, 0.9646, 0.965, 0.9654, 0.9658, 0.9662, 0.9666, 0.967, 0.9674, 0.9678, 
        0.9681, 0.9685, 0.9689, 0.9693, 0.9697, 0.97, 0.9704, 0.9708, 0.9711, 0.9715, 
        0.9719, 0.9722, 0.9726, 0.9729, 0.9733, 0.9736, 0.974, 0.9743, 0.9747, 0.975, 
        0.9754, 0.9757, 0.976, 0.9764, 0.9767, 0.977, 0.9774, 0.9777, 0.978, 0.9783, 
        0.9786, 0.9789, 0.9793, 0.9796, 0.9799, 0.9802, 0.9805, 0.9808, 0.9811, 0.9814, 
        0.9817, 0.982, 0.9823, 0.9825, 0.9828, 0.9831, 0.9834, 0.9837, 0.9839, 0.9842, 
        0.9845, 0.9847, 0.985, 0.9853, 0.9855, 0.9858, 0.9861, 0.9863, 0.9866, 0.9868, 
        0.9871, 0.9873, 0.9875, 0.9878, 0.988, 0.9883, 0.9885, 0.9887, 0.989, 0.9892, 
        0.9894, 0.9896, 0.9898, 0.9901, 0.9903, 0.9905, 0.9907, 0.9909, 0.9911, 0.9913, 
        0.9915, 0.9917, 0.9919, 0.9921, 0.9923, 0.9925, 0.9927, 0.9929, 0.993, 0.9932, 
        0.9934, 0.9936, 0.9937, 0.9939, 0.9941, 0.9942, 0.9944, 0.9946, 0.9947, 0.9949, 
        0.995, 0.9952, 0.9953, 0.9955, 0.9956, 0.9958, 0.9959, 0.996, 0.9962, 0.9963, 
        0.9964, 0.9966, 0.9967, 0.9968, 0.9969, 0.9971, 0.9972, 0.9973, 0.9974, 0.9975, 
        0.9976, 0.9977, 0.9978, 0.9979, 0.998, 0.9981, 0.9982, 0.9983, 0.9984, 0.9985, 
        0.9986, 0.9986, 0.9987, 0.9988, 0.9989, 0.9989, 0.999, 0.9991, 0.9991, 0.9992, 
        0.9993, 0.9993, 0.9994, 0.9994, 0.9995, 0.9995, 0.9996, 0.9996, 0.9997, 0.9997, 
        0.9997, 0.9998, 0.9998, 0.9998, 0.9999, 0.9999, 0.9999, 0.9999, 0.9999, 1, 
        1, 1, 1, 1, 1, 1};

        const static uint64 mask = max-1; 
        return logvals[h.first&mask]*cosvals[h.second&mask];

        // Note that we are just using the Box-Muller transform to compute the result.  In
        // particular, we are doing this (where u1 and u2 are uniform random variables in
        // the range [0,1]): 
        //    return sqrt(-2*log(u1)) * cos(2*PI*u2);
        // It is just that we use table lookups to avoid calling sqrt(), log() and cos().
    }

// ----------------------------------------------------------------------------------------

}

#endif // DLIB_RANDOM_HAsHING_Hh_

